Real Analysis
MIT OpenCourseWare's introduction to mathematical analysis covers convergence of sequences and series, continuity, differentiability, and the Riemann integral, then moves into sequences and series of functions, uniform convergence, and the conditions under which limit operations can be interchanged. The course builds from the structure of the real numbers and uses that foundation to teach rigorous proof writing rather than computation. Materials include lecture notes, problem sets, and exams consistent with MIT's standard OCW format, letting students work through the same assignments used in the on-campus class. The emphasis throughout is on abstract reasoning: why theorems hold, not just how to apply them. As with other OCW offerings, all materials are free under a Creative Commons license, there is no instructor interaction or certificate, and the course functions as self-study material for anyone with a solid grounding in calculus who wants to understand its theoretical underpinnings.